function r_high = r_high_for_mode(m, CONSTS)

    r_high=1;
    step=1e-1;
    min=1e+3;
    [~,  E_phi1,  E_z_outside] = func_E_outside(1, m, CONSTS);
    [~,  E_phi,  E_z_outside]  = func_E_outside(1, m, CONSTS);
    while abs(E_phi1)/abs(E_phi) < min
        r_high=r_high+step;
        [~,  E_phi,  E_z_outside] = func_E_outside(r_high, m, CONSTS);
%     [H_rho_outside,  H_phi_outside,  H_z_outside] = func_H_outside(r2_vec, m, CONSTS);
    end

end